Variational Monte Carlo study of gapless spin liquid in the spin-$1/2$ XXZ antiferromagnetic model on the kagome lattice

Abstract

By using the variational Monte Carlo technique, we study the spin-$1/2$ XXZ antiferromagnetic model (with easy-plane anisotropy) on the kagome lattice. A class of Gutzwiller projected fermionic states with a spin Jastrow factor is considered to describe either spin liquids (with $U(1)$ or $Z_2$ symmetry) or magnetically ordered phases (with $\mathbf{q}=(0,0)$ or $\mathbf{q}=(4\pi /3,0)$). We find that the magnetic states are not stable in the thermodynamic limit. Moreover, there is no energy gain to break the gauge symmetry from $U(1)$ to $Z_2$ within the spin-liquid states, as previously found in the Heisenberg model. The best variational wave function is therefore the $U(1)$ Dirac state, supplemented by the spin Jastrow factor. Furthermore, a vanishing $S=2$ spin gap is obtained at the variational level, in the whole regime from the $XY$ to the Heisenberg model.

7 pages, 7 figures

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• Generic nearest-neighbour kagome model: XYZ & Dzyaloshinskii-Moriya, and comparison to pyrochlore
• Doping quantum spin liquids on the Kagome lattice
• Spin-1/2 kagome Heisenberg antiferromagnet: Machine learning discovery of the spinon pair density wave ground state